Math 319, Topics in Algebra: Lie Groups, fall 2003

BIBLIOGRAPHY

Photocopied material:

Physics background and motivation.

Taylor, E.F. and Wheeler, J.A., {\em Spacetime Physics}, W.H. Freeman (1966),

pp. 1-5, 22-27, 39-42, 59.

Primary resources on Lie groups.

Artin, M., Algebra, Prentice Hall (1991), pp. 123-154, 270-292, pp. 300-306.

Curtis, M.L., Matrix Groups, Springer Verlag, Universitext (1979), pp. 45-51.

Howe, R., ``Very Basic Lie Theory," American Mathematical Monthly,, vol. 90, no. 9 (1983), pp. 600-623.

Tidbits from linear algebra and multivariable calculus.

McCallum, W.B. et al, Multivariable Calculus, John Wiley and Sons (1997), pp. 85-90.

Osserman, R., Two-dimensional Calculus, Harcourt, Brace and World, Inc. (1968), pp. 232-240.

History.

Altman, S.L., Rotations, Quaternions and Double Groups, Oxford University Press (1986), pp. 9-19.

Newman, J.R., ed., The World of Mathematics, Simon and Schuster (1956), pp. 161-163.

Yaglom, I.M. (translated by S. Sossensky, edited by H. Grant and A. Shenitzer),

Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth

Century, Birkhauser (1988), pp. 22-27, 85-93, 95-97.

Other references:

Burn, R.P. Groups: A Path to Geometry, Cambridge University Press (1985).

Callahan, J.J., The geometry of spacetime: an introduction to special and general relativity, Springer Verlag (2000).

Gorenstein, D., Finite Groups, Harper and Row (1968).

Hausner, M. and Schwartz, J.T., Lie Groups; Lie Algebras, Gordon and Breach, Notes on Mathematics and its Applications (1968).

Howe, R. and Barker, W., Continuous Symmetry: From Euclid to Einstein, manuscript (2000).

Humphreys, J.E., Introduction to Lie Algebras and Representation Theory, Springer Verlag, Graduate Texts in Mathematics (1972).

Ise, M. and Takeuchi, M., Lie Groups I, American Mathematical Society, Translations of Mathematical Monographs, vol. 85 (1991).

Mumford, D. et al, Indra's Pearls: The Vision of Felix Klein, Cambridge University Press (2002).

Rossman, W. Lie Groups: An Introduction Through Linear Groups, Oxford University Press (2002).

Sattinger, D.H. and Weaver, O.L., Lie Groups and Algebras with Applications toPhysics, Geometry and Mechanics, Springer Verlag, Applied Mathematical Sciences no. 61 (1986).

Singer, S.F., Symmetry in Mechanics: A Gentle, Modern Introduction, Birkhauser (2001).

Zulli, L., ``Charting the 3-sphere---an exposition for undergraduates," Amer. Math.

Monthly vol. 103, no. 3 (1996), 221-229.